涓浗绉戝闄㈡暟瀛︿笌绯荤粺绉戝鐮旂┒闄㈡湡鍒婄綉

鏁板瀛︽姤 鈥衡�� 2005, Vol. 48 鈥衡�� Issue (2): 397-402.DOI: 10.12386/A2005sxxb0048

鈥� 璁烘枃 鈥� 涓婁竴绡�    涓嬩竴绡�

骞夸箟骞傜骇鏁扮幆鐨凪orita瀵瑰伓

鍒樹徊濂�   

  1. 瑗垮寳甯堣寖澶у鏁板绯� 鍏板窞730070
  • 鏀剁鏃ユ湡:1900-01-01 淇洖鏃ユ湡:1900-01-01 鍑虹増鏃ユ湡:2005-03-15 鍙戝竷鏃ユ湡:2005-03-15
  • 閫氳浣滆��: 鍒樹徊濂�

Morita Duality for the Rings of Generalized Power Series

Zhong Kui LIU   

  1. Zhong Kui LIU Department of Mathematics, Northwest Normal University, Lanzhou 730070, P. R. China
  • Received:1900-01-01 Revised:1900-01-01 Online:2005-03-15 Published:2005-03-15
  • Contact: Zhong Kui LIU

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鎽樿锛� 璁続,B鏄湁鍗曚綅鍏冪殑鐜�, (S,鈮�)鏄湁闄愮敓鎴愮殑Artin鐨勪弗鏍煎叏搴忓购鍗婄兢, AMB鏄弻妯�.鏈枃璇佹槑浜嗗弻妯[AS,鈮][MS,鈮[[BS,鈮]瀹氫箟涓�涓狹orita瀵瑰伓褰撲笖浠呭綋 AMB瀹氫箟涓�涓狹orita瀵瑰伓涓擜鏄乏noether鐨�,B鏄彸noether鐨�.鍥犳A涓婄殑骞� 涔夊箓绾ф暟鐜痆[AS,鈮]鍏锋湁Morita瀵瑰伓褰撲笖浠呭綋A鏄乏noether鐨勪笖鍏锋湁鐢卞弻妯MB 璇卞鐨凪orita瀵瑰伓,浣垮緱B鏄彸noether鐨�.

鍏抽敭璇�: 骞夸箟骞傜骇鏁扮幆, 宸︾嚎鎬х揣妯�, Morita瀵瑰伓

Abstract: Let A, B be associative rings with identity, and (S,鈮�) a strictly totally ordered monoid which is also Artinian and finitely generated. For any bimodule AMB, we show that the bimodule [[AS,鈮][MS,鈮[[BS,鈮] defines a Morita duality if and only if AMB defines a Morita duality and A is left noetherian, B is right noetherian. As a corollary, it is shown that the ring [[AS,鈮] of generalized power series over A has a Morita duality if and only if A is a left noetherian ring with a Morita duality induced by a bimodule AMB such that B is right noetherian.

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